"Blood spurted from Malfoy's face and chest as though he had been slashed with an invisible sword. He staggered backward and collapsed onto the waterlogged floor with a great splash, his wand falling from his limp right hand. "No —" gasped Harry. Slipping and staggering, Harry got to his feet and plunged toward Malfoy, whose face was now shining scarlet, his white hands scrabbling at his blood-soaked chest."
Sectumsempra is a Dark Arts curse invented by Severus Snape (under his alias of "The Half-Blood Prince") for the use against his enemies, and it soon became one of his specialities. Easily a curse of the highest level, when uttered, its effect is the equivalent of an invisible sword, which can be used by the caster to slash the victim(s) from a distance. The injuries appear to follow the movements of the caster's wand, making it very deadly to use on vital parts, and thus inflicts the most damage if cast with rapid waving movements. It works best on living targets and has no noticeable effect on inanimate objects or dead ones, such as Inferi, other than slashing them pointlessly.
Wounds inflicted by the curse can be cured by the spell Vulnera Sanentur.[1] If the wounds caused are of a certain severity, it may take three castings to heal the victim acceptably: the first time the flow of blood eases up; the second time it causes the wounds to knit; the third time removes the worst effects of the curse. The victim would still require medical treatment, and if Dittany is applied immediately, scarring can be avoided.
Though the healing spell can heal the wounds, and Dittany can prevent scars, any body parts that have been severed by this curse cannot be grown back, as seen when George Weasley lost his left ear to it.
"You dare use my own spells against me, Potter? It was I who invented them — I, the Half-Blood Prince! And you'd turn my inventions on me, like your filthy father, would you? I don't think so… no!"
While attending Hogwarts School of Witchcraft and Wizardry and being harassed by James Potter, Snape used the spell while fighting him. James Potter, however, did not receive the full brunt of the attack due to Snape's lack of aim and nonverbal use; resulting in one deep gash upon his cheek as opposed to potentially fatal wounds to his body.
In a duel with Draco Malfoy, Harry, not knowing exactly what the curse did, used it on him when Malfoy was poised to use a Cruciatus Curse. This resulted in Malfoy almost dying much to Harry's horror, proving how deadly the curse can be.
While in the Horcrux cave, Harry used the spell on an army of Inferi left to protect the Horcrux. This was to no avail, as Inferi could neither feel the gashes inflicted upon them nor lose any blood from the cuts.
During the Battle of the Astronomy Tower, Harry attempted to use the spell against Snape as he fled the school with the Death Eaters. Snape, however, deflected the spell easily, and revealed that he was the spell's creator, the "Half-Blood Prince."
During the Battle of the Seven Potters, Snape, attempting to stop a Death Eater from cursing Remus Lupin, aimed a Sectumsempra curse at him, but it accidentally struck George Weasley. George lost an ear due to his injury, which could not be healed because it was caused by a curse.
Etymology
Sectumsempra derives from the Latin sectum, "having been cut" (comparable to the English word "section" or "segmented"), and possibly semper, "always." It can be translated as "always cutting" or "sever forever", the latter being a pun on Snape's first name, Severus.
Behind the scenes
Voldemort casting this spell on Severus Snape, the creator of this spell, moments before Nagini finishes him off.
Sectumsempra, like Levicorpus, probably escaped Snape's secrecy too, as Lupin mentions it as "always a speciality of Snape's." It may also be possible that Lupin did not know the verbal form of the spell before the Battle of the Seven Potters, but heard it during the battle and only detected it by its effect he had seen before.
The spell was engineered by Snape to use on enemies. It is possible that while inventing it, Snape's intention was to use it on his enemies back then, the Marauders.